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Ayyıldız and Ayyıldız (2017). “Kinematic milling,” BioResources 12(4), 9326-9337. 9326

Development of a 3-axis Parallel Kinematic Machine for Milling Wood Material – Part 1: Design

Elmas Aşkar Ayyıldız a and Mustafa Ayyıldız b,*

A 3-axis parallel kinematic machine tool and advanced control system with programming in G-code for the milling of wood material are described in detail. This parallel kinematic machine is based on a 3-PSS (prismatic link, spherical link, and spherical link) parallel mechanism. A programming system and control based on a real-time PC windows platform and Mach3 software system was implemented for this tool. Finally, a model application of a programming system developed for a three-degree-of-freedom linear delta parallel machine was presented, and the workability for milling wood material (medium-density fibreboard) was shown.

Keywords: Parallel kinematic machine; G-code; Milling wood material

Contact information: a: Institute of Science and Technology, Karabük University, Karabük, Turkey;

b: Manufacturing Engineering Department of Technology Faculty, Düzce University, Düzce, Turkey;

*Corresponding author: [email protected]

INTRODUCTION

Wood machining is strongly influenced by wood texture. Thus, it is a very

important field of research to achieve optimum wood machining conditions (Aguilera et

al. 2000). Milling is a machining operation regularly used in manufacturing parts of wood.

In previous literature, metal milling has been studied broadly, but medium-density

fibreboard (MDF) milling has not received much attention. Many works (Aguilera et al.

2000; Gordon and Hillery 2003; Lin et al. 2006; Davim et al. 2009; Vančo et al. 2017),

when reporting about the machining of wood material, have shown that the machinability

is dependent upon the cutting tool, the cutting mechanics, and the workpiece material.

Parallel Kinematic Machines (PKMs) are frequently used in many industrial

applications that require high precision demanded by the latest developments in

technology. This is because parallel manipulators have such capabilities as a higher

payload, high rigidity and accuracy, good stability, usability in high-speed applications, a

good dynamic performance, and precise positioning. The PKMs are frequently employed

in industrial applications such as medical operations, game simulators, oil platforms, heavy

freight transport, light metal machining, polishing, cutting, shaping and assembly

operations, and flight simulators.

Having reviewed the literature, Gao et al. (2002) presented a design and

innovations for new variants of 2 degree-of-freedom (DOF), 3 DOF, 4 DOF, and 5 DOF

parallel mechanisms. In their study, Liu et al. (2005) proposed the family of 3-degree-of-

freedom parallel manipulators with a new high-revolution capacity to overcome low-

revolution capabilities of existing parallel manipulators. Budde et al. (2007) presented

design problems (singularity) and the optimization of a linear delta robot (workspace,

rigidity, precision of varying rod lengths) and implemented their model application in

furtherance of this work (Budde et al. 2008).



Stan et al. (2008) presented a multi-objective optimum design procedure to triglide

and delta robot features, such as workspace boundaries, rigidity, and transmission quality

index (speed, force, and power characteristics), which are the optimal design criteria for 3-

DOF parallel robots. Corbel et al. (2008) presented the design and optimization of a parallel

machine tool by combining a real 3-DOF robot (linear delta) with 6-DOF measuring

parallel robots. Yuan et al. (2008) proposed optimal design methods for the linear delta

robot to obtain a specified cuboid workspace.

Kelaiaia et al. (2012) presented an illustrative application of the methodology

developed for a linear delta parallel robot with 3-DOF. This methodology involves the

geometric, kinematic, and dynamic models of the selected structure. It estimates

performance criteria (workspace, rigidity, kinematic, and dynamic performance),

determines the boundaries of the robot structure, creates mathematical formulae of the

optimization problem, and uses a genetic algorithm utility for the solution of the problem.

Patel and George (2012) compared various criteria, such as structures and workspaces, for

serial and parallel manipulators. Niu et al. (2013) presented the dynamics and control of a

novel 3-DOF parallel manipulator with actuation redundancy. Zeng et al. (2014)

introduced the structure and constraint design of a 3-DOF translational parallel

manipulator. Lin et al. (2015) investigated the design and implementation of the delta

parallel robot, covering the entire mechatronic process, involving kinematics, control

design, and optimizing methods. Xie et al. (2016) proposed a 6-DOF hybrid mechanism

for the development of a turbine blade grinding machine. The conceptual design was

presented, and the singularity of the 3-DOF parallel module was analyzed. Xu et al. (2017)

presented a novel hybrid machine with 6-DOF serial-parallel topological structure used as

an ultra-precision polishing equipment.

Today, the majority of university laboratories, research institutes, and enterprises

do not have PKMs. This is because education and training costs for a novel technology like

PKM are high. There are rare studies in the literature on a low-cost 3-DOF parallel

kinematic machine aimed at contributing to practical experiences in the use of PKM

(Glavonjic et al. 2009). Yang and Hong (2001) developed a real-time intercept-based three-

dimensional (3D) linear and circular interpolation software to achieve simultaneous 3-axis

motion on the PC-NC milling machine. Gordon and Hillery (2005) developed a low-cost

bridge-type X/Y motion system. In this system, the CNC controller is controlled by an

interface that supports G-codes written in C ++. Kanaan et al. (2009) obtained inverse and

forward kinematic equations for a serial-parallel 5-axis machine, which they called a

VERNE machine tool. Here, symbolic methods to calculate all kinematic solutions are

proposed.

Guo et al. (2012) developed a universal numeric control (NC) program processor

for CNC systems aimed at processing various types of NC software because most CNC

manufacturers use their own custom functions in NC software. In this study, the purpose

is to transform the G-codes produced by any CAM software for controlling a linear delta

parallel machine, one of the PKM structures, into a new G-code structure interpretable by

the robot. For this purpose, an inverse kinematic model was developed for the linear delta

parallel machine, and G-codes were transformed into a meaningful code system for this

structure through a designed interface. The new codes produced were transferred to the

PKM structure in a sequence to control the system.



EXPERIMENTAL

Description and Kinematics of the Mechanism Figure 1 shows the geometric definitions for the linear delta parallel machine. As

can be seen in Fig. 2, the machine is in the form of a 3-degree-of-freedom parallel robot of

3-PSS (prismatic link, spherical link, spherical link) type (Gao et al. 2002). The robot

consists of arms integrated into the fixed platform and a mobile platform. The mobile

platform and the fixed platform are coupled to each other by 3 kinematic chains arranged

at an angle of αi. Each kinematic chain was jointed with 2 parallel rods of length L (with a

distal and proximal spherical link) and with a linear actuator (Gao et al. 2002).

The mobile platform always remained parallel to the fixed platform. The prismatic

motion of the mobile platform was provided by the combined motion of all 3 actuators. In

the literature, there are various studies on the kinematic modeling of a linear delta robot

(Company and Pierrot 2002; Righettini et al. 2002; Liu et al. 2004; Kelaiaia et al. 2012;

Xie et al. 2016).

Fig. 1. Geometric definition of the linear delta robot (Gao et al. 2002)

The geometric definitions of the linear delta robot are given below (Gao et al.

2002),

{R0}: (00--x0, y0, z0): “00” is the reference frame for the fixed platform, the center of the

equilateral triangle 010203, and also the center of the circle with radius Rb.

{Rp}: (P—xn, yn, zn): “P” is the reference frame for the mobile platform, the center of the

equilateral triangle B1B2B3, and also the center of the circle with radius Rn.

q1, q2, q3: Links the variables for stroke control of 3 linear actuators.

Rb: Is the radius of the circle centered at 00, and the distance between 0i and 00, and‖000𝑖‖ =𝑅𝑏 , 𝑖 = 1,2,3



Rn: Is the radius of the circle centered at P, the distance between “P”,Bi, and the center of

the mobile platform, and ‖𝑃𝐵𝑖‖ = 𝑅𝑛, 𝑖 = 1,2,3.

The kinematic model for the linear delta robot refers to the position and the

orientation of the end effector in relation to the reference frame (R0) and ‖𝐴𝑖𝐵𝑖‖ = 𝐿.

AiBi2- L2= 0, i = 1, 2, 3 (1)

Coordinates of Bi in the reference frame for the movable platform are given in Eq. 2,

[𝐵𝑖]𝑠𝑎𝑏𝑖𝑡 = [𝑥 + 𝑅𝑛𝑐𝑜𝑠𝛼𝑖

𝑦 + 𝑅𝑛𝑠𝑖𝑛𝛼𝑖

𝑧] (2)

and coordinates of Ai in the reference frame for the fixed platform are given in Eq. 3,

[𝐴𝑖]𝑠𝑎𝑏𝑖𝑡 = [𝑅𝑏𝑐𝑜𝑠𝛼𝑖

𝑅𝑏𝑠𝑖𝑛𝛼𝑖

𝑞𝑖

] (3)

𝛼𝑖 =2𝜋

3(𝑖 − 1), 𝑖 = 1, 2, 3 (4)

Using Eq. 1 to build the expression of the inverse kinematic model, Eq. 5 was obtained.

𝑞𝑖 = 𝑧 + √𝐿2 − (𝑥 − (𝑅𝑏 − 𝑅𝑛)𝑐𝑜𝑠𝛼𝑖)2 − (𝑦 − (𝑅𝑏 − 𝑅𝑛)𝑠𝑖𝑛𝛼𝑖)2 (5)

To build the forward kinematic model for the linear delta robot, Eq. 6 should be solved

with respect to X, Y, and Z (Stan et al. 2008),

{𝐹𝑧2 + 2𝐺𝑧 + 𝐻 = 0

𝑦 = 𝐴𝑧 + 𝐵𝑥 = 𝐶𝑧 + 𝐷

} (6)

where:

𝑧1,2 =−2𝐺±√2𝐺2−4𝐹𝐻

2𝐹 (7)

The solution adopted was 𝑧 = min (𝑧1, 𝑧2)

𝐴 =(𝑞2−𝑞3)

√3(𝑅𝑏−𝑅𝑛) (8)

𝐵 =𝑞3

2−𝑞22

2√3(𝑅𝑛−𝑅𝑏) (9)

𝐶 =2(𝑞2−𝑞1)−𝐴(𝑅𝑛−𝑅𝑏)√3

3(𝑅𝑏−𝑅𝑛) (10)

𝐷 =𝑞1

2−𝑞22−𝐵√3(𝑅𝑛−𝑅𝑏)

3(𝑅𝑏−𝑅𝑛) (11)

𝐸 = (𝑅𝑛 − 𝑅𝑏) + 𝐵 (12)

𝐹 = 𝐴2 + 𝐶2 + 1 (13)

𝐺 = 𝐴𝐸 + 𝐶𝐷 − 𝑞1 (14)

𝐻 = 𝐸2 + 𝐷2 + 𝑞12 − 𝐿2 (15)

Applying the above equations to Eq. 6, the forward kinematic model for the linear delta

robot was formulated.



Fig. 2. Link scheme for the linear delta robot

Control Structure of Linear Delta Parallel Machine Integrated operations of the system were ensured via a software system appropriate

for controlling the linear delta parallel machine. The interface designed with an inverse

kinematic modeling of linear delta and G-codes were transformed into a meaningful code

system for this structure. The codes produced were transferred to the PKM structure in a

sequence to control the system. Figure 3 shows the control structure of the linear delta

parallel machine.

Fig. 3. Control flowchart of the linear delta parallel machine

Based on Fig. 3, it is possible to plan the orbit of the linear delta parallel machine.

By designing the model of any physical object, the object’s build codes were produced



with the help of the CAM software. Here, build codes produced with the CAM software

were formed according to the Cartesian space. Adapting these codes in the Cartesian space

to the build environment, motors linked to the X, Y, and Z axes were linearly driven. The

codes produced for the Cartesian structure were not suitable for the motional structure of

the linear delta parallel machine structure within the workspace. Due to the linear motion

of the arms A1, A2, and A3 of the linear delta, and due to the prismatic motions occurring

at the joint of these arms, transformation into a coding system interpretable by the Cartesian

structure was necessary. Therefore, a new code system was created based on appropriate

CAM codes through an interface according to the prismatic motion of arms A1, A2, and A3

by linear delta, and by employing the kinematic equations for this structure. The new codes

produced were run on the Mach3 software (Valentino and Goldenberg 2006) for

controlling the linear delta parallel machine. Control of the linear delta parallel machine

was conducted by repeating this sequence.

RESULTS AND DISCUSSION

Producing CAM Codes Using the Mastercam X5 software (Valentino, and Goldenberg 2006), the build

codes of an object designed in any CAD software were produced. In producing the build

codes with Mastercam X5, the machine type selected was “Default”. The reason for this is

that there is no machine type available for the linear delta parallel machine. Figure 4 shows

a sample code produced with Mastercam X5.

Fig. 4. Sample code produced with Mastercam X5

Code Transformation with the Interface Developed

Because the codes produced with Mastercam X5 in Fig. 4 were appropriate for

machine types of the Cartesian structure, these codes were transformed into the motion



space of the parallel delta parallel machine that had a parallel structure. The inverse

kinematic equations were employed. The interface was developed in Visual Studio 2015

(Fig. 5).

Fig. 5. The interface developed

Fig. 6. Flowchart of the interface system developed

The flowchart of the interface system developed is shown in Fig. 6. In this interface,

an algorithm was developed for codes G0, G1, G2, and G3. For codes G0 and G1, a new



code was produced by performing an inverse kinematic calculation with X, Y, Z values in

the corresponding row. Using the start and end points of the arc as a reference for the code

G2, the arc path was pixelated for a clockwise linear interpolation with X, Y, Z and I, J, K

values. These pixels were calculated based on the arc angle and hypotenuse found. The

same applied to code G3. When the interface recognized the codes G2 and G3, the

algorithm ran and the new code was transformed as a code G1. Figure 7 shows G2 and G3

circular interpolation parameters (Petrovic et al. 2017).

(a) (b)

Fig. 7. G2 and G3 circular interpolation parameters

The radius of the arcs shown in Fig. 7 is given in Eq. 16, while the arc angles are

given in Eqs. 17 and 18 (Petrovic et al. 2017),

, (16)

(17)

(18)

where x1, y1, and z1 are the arc start coordinates, x2, y2, and z2 are the arc end coordinates,

xc, yc, and zc are central coordinates of the circular interpolation, r is the radius of the

circular interpolation (o), α0 is the start angle of the circular interpolation (o), and α1 is the

circular interpolation angle (o).



Running New Codes with Mach3 The new codes produced were run using the Mach3 software. The Mach3 software

communicated with the AKZ250 USB control card to guide the motors. As practice, the

contouring of square, circle, and triangle geometries was performed. Figure 8 shows a

model application. Table 1 shows the G-codes produced for the Cartesian structure, and

the new G-codes transformed into a delta structure through the interface developed.

Fig. 8. Model contouring for a square, circle, and triangle

Table 1. The G-codes Produced for the Cartesian Structure

Cartesian G-codes G-codes for Delta Structure

% O0000(TUM) N102 G0 G17 G40 G49 G80 G90 N104 T225 M6 N106 G0 G90 G54 X-62.5 Y2.5. S5730 M3 N108 G43 H225 Z10. N110 G1 Z-1. F859.5 N112 X2.5 F250. N114 Y-62.5 N116 X-62.5 N118 Y2.5 N120 G0 Z10. N122 X-7.5 Y-30. N124 G1 Z-1. F859.5 N126 G3 X-30. Y-7.5 I-22.5 J0. F250. - - - - N154 M30 %

% O0000(TUM) N102 G0 G17 G40 G49 G80 G90 N104 T225 M6 N106 G0 G90 G54 X-30,29 Y21,67 Z19,48 S5730 M3 N108 G43 H225 X-30,29 Y21,67 Z19,48 N110 G1 X-41,29 Y10,67 Z8,48 F859.5 N112 X0,28 Y-0,54 Z-2,8 F250. N114 X-5,24 Y-37,14 Z20,33 N116 X-47,55 Y-24,69 Z30,94 N118 X-41,29 Y10,67 Z8,48 N120 G0 X-30,29 Y21,67 Z19,48 N122 X4,71 Y-3,15 Z23,84 N124 G1 X-6,29 Y-14,15 Z12,84 F859.5 N126 G1 X-6,21 Y-13,51 Z12,44 F250 N126 G1 X-6,16 Y-12,86 Z12,06 N126 G1 X-6,15 Y-12,21 Z11,68 N126 G1 X-6,18 Y-11,56 Z11,32 N126 G1 X-6,24 Y-10,9 Z10,97 N126 G1 X-6,34 Y-10,24 Z10,64 N126 G1 X-6,47 Y-9,58 Z10,32 N126 G1 X-6,64 Y-8,93 Z10,01 N126 G1 X-6,85 Y-8,28 Z9,73 - - - N154 M30 %



CONCLUSIONS

1. This paper introduced a novel design of a linear delta parallel machine for milling

wood material. The development of the machine involved the development of the

mechanism, as well as both its hardware and software.

2. An inverse kinematic model was developed for the linear delta parallel machine,

and G-codes were transformed into a meaningful code system for this structure

through the designed interface. The new codes produced were transferred to the

linear delta structure in a sequence to control the system.

3. Finally, by developing a model application of a programming system developed for

a 3 degree-of-freedom linear delta parallel machine, the workability for milling

wood material (medium-density fibreboard) was shown.

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Article submitted: June 23, 2017; Peer review completed: October 14, 2017; Revised

version received and accepted: October 18, 2017: Published: October 25, 2017.

DOI: 10.15376/biores.12.4.9326-9337

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